{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,17]],"date-time":"2026-10-17T06:41:55Z","timestamp":1792219315716,"version":"4.4.0"},"reference-count":25,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T00:00:00Z","timestamp":1792108800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T00:00:00Z","timestamp":1792108800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100009104","name":"Department of Health Research, India","doi-asserted-by":"publisher","award":["R.11012\/03\/2021\u2010GIA\/HR"],"award-info":[{"award-number":["R.11012\/03\/2021\u2010GIA\/HR"]}],"id":[{"id":"10.13039\/501100009104","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Pharmaceutical Statistics"],"published-print":{"date-parts":[[2026,11]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>\n                    Joint modeling provides a robust statistical framework for simultaneously modeling longitudinal covariate and time\u2010to\u2010event outcome. Apart from the interdependence between longitudinal and survival outcomes there may exist some unobserved random heterogeneity which can be modeled using a joint frailty model (JFM). Unlike existing JFMs, where two survival events are modeled using a frailty, our framework incorporates frailty into the survival sub\u2010model to accommodate an additional source of variation at the survival endpoint. So here we developed a novel JFM and estimated the parameters using maximum\u2010likelihood estimation method. The analyses were performed using R Software and illustrated using colorectal cancer data. The frailty component was introduced in colorectal cancer data to account for the unobserved variability in survival risk beyond the observed clinical characteristics. The highly significant frailty variance confirmed the presence of unobserved heterogeneity in survival outcomes. When compared with the standard Joint model (JM), the JFM demonstrated improved model fit and captured additional unexplained heterogeneity among individuals, leading to more precise hazard estimates. Further we conducted Monte Carlo simulations to compare the performance of the proposed model under various simulation scenarios (censoring [20% and 50%], frailty variance (\u22480, 0.5, 1), and sample sizes [\n                    <jats:italic>n<\/jats:italic>\n                    \u2009=\u2009100, 250, 500]). Performance was assessed using bias, root mean squared error and model fit indices. The findings highlight the importance of incorporating the frailty term in joint modeling, particularly in cancer prognostic studies where individual heterogeneity plays a crucial role.\n                  <\/jats:p>","DOI":"10.1002\/pst.70126","type":"journal-article","created":{"date-parts":[[2026,10,17]],"date-time":"2026-10-17T06:07:11Z","timestamp":1792217231000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Joint Model for Assessing the Effect of Frailty and Longitudinal Measures in Time\u2010To\u2010Event Outcome"],"prefix":"10.1002","volume":"25","author":[{"given":"Anand","family":"Hari","sequence":"first","affiliation":[{"name":"Manipal Academy of Higher Education  Manipal Karnataka India"},{"name":"Division of Cancer Epidemiology and Biostatistics Regional Cancer Centre  Thiruvananthapuram Kerala India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Divya","family":"Dennis","sequence":"additional","affiliation":[{"name":"Manipal Academy of Higher Education  Manipal Karnataka India"},{"name":"Division of Cancer Epidemiology and Biostatistics Regional Cancer Centre  Thiruvananthapuram Kerala India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6393-6357","authenticated-orcid":false,"given":"Jagathnath Krishna Kumara Pillai Mohanan","family":"Nair","sequence":"additional","affiliation":[{"name":"Division of Cancer Epidemiology and Biostatistics Regional Cancer Centre  Thiruvananthapuram Kerala India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aleyamma","family":"Mathew","sequence":"additional","affiliation":[{"name":"Division of Cancer Epidemiology and Biostatistics Regional Cancer Centre  Thiruvananthapuram Kerala India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,10,16]]},"reference":[{"issue":"1","key":"e_1_2_11_2_1","doi-asserted-by":"crossref","first-page":"330","DOI":"10.2307\/2533118","article-title":"A Joint Model for Survival and Longitudinal Data Measured With Error","volume":"53","author":"Wulfsohn M. S.","year":"1997","journal-title":"Biometrics"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/1.4.465"},{"key":"e_1_2_11_4_1","doi-asserted-by":"crossref","DOI":"10.1201\/b12208","volume-title":"Joint Models for Longitudinal and Time\u2010To\u2010Event Data: With Application","author":"Rizopoulos D.","year":"2012"},{"key":"e_1_2_11_5_1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev\u2010statistics\u2010030718\u2010105048"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.1177\/09622802251320793"},{"key":"e_1_2_11_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00985760"},{"key":"e_1_2_11_8_1","doi-asserted-by":"publisher","DOI":"10.1177\/0962280212445839"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11222\u2010025\u201010647\u20101"},{"key":"e_1_2_11_10_1","doi-asserted-by":"publisher","DOI":"10.4310\/sii.2010.v3.n2.a6"},{"key":"e_1_2_11_11_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006\u2010341X.2004.00244.x"},{"key":"e_1_2_11_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.201200160"},{"key":"e_1_2_11_13_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.7682"},{"key":"e_1_2_11_14_1","doi-asserted-by":"publisher","DOI":"10.1080\/02664763.2022.2096209"},{"key":"e_1_2_11_15_1","doi-asserted-by":"publisher","DOI":"10.1080\/10543406.2026.2626062"},{"key":"e_1_2_11_16_1","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.201900113"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.10053"},{"key":"e_1_2_11_18_1","doi-asserted-by":"publisher","DOI":"10.1177\/0962280220921889"},{"key":"e_1_2_11_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2019.105259"},{"key":"e_1_2_11_20_1","doi-asserted-by":"publisher","DOI":"10.1515\/sagmb\u20102023\u20100038"},{"key":"e_1_2_11_21_1","doi-asserted-by":"publisher","DOI":"10.3390\/cancers16081530"},{"key":"e_1_2_11_22_1","doi-asserted-by":"publisher","DOI":"10.25107\/2474\u20101663\u2010v9\u2010id2046"},{"key":"e_1_2_11_23_1","doi-asserted-by":"publisher","DOI":"10.1093\/ije\/dyab047"},{"key":"e_1_2_11_24_1","doi-asserted-by":"publisher","DOI":"10.1214\/25\u2010AOAS2098"},{"key":"e_1_2_11_25_1","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxab037"},{"key":"e_1_2_11_26_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.9829"}],"container-title":["Pharmaceutical Statistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/pst.70126","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/pst.70126","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/pst.70126","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,17]],"date-time":"2026-10-17T06:07:12Z","timestamp":1792217232000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/pst.70126"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,16]]},"references-count":25,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2026,11]]}},"alternative-id":["10.1002\/pst.70126"],"URL":"https:\/\/doi.org\/10.1002\/pst.70126","archive":["Portico"],"relation":{},"ISSN":["1539-1604","1539-1612"],"issn-type":[{"value":"1539-1604","type":"print"},{"value":"1539-1612","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,16]]},"assertion":[{"value":"2025-10-15","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-09-07","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-10-16","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70126"}}